One method for constructing an alarm or security screen, includes weaving a mesh with several parallel insulated conductive wire security strands, and then cutting a rectangular sheet therefrom. As described in my earlier U.S. Pat. No. 3,051,935, opposite sides of the mesh sheet can be trimmed away to leave projecting lengths of the security strands. The security strands can be connected together and to a plug and tamper switch, to provide a conductive path that permits current to flow in a sinuous path covering the screen area, between the plug and switch. The edges of the mesh then can be held to a screen frame by rolling them into a frame by forcing a resilient rod-shaped spline over the mesh and into a groove in the frame. The inner connections of the security strands are sealed on opposite ends to keep out moisture. Considerable labor is involved in trimming away the mesh, in making the interconnections of the security strands, and in installing and sealing the screen edges. Furthermore, if the mesh is damaged, the entire screen assembly which includes the frame, normally has to be returned to the factory for repair, because of the intricacies in installing the mesh into the frame and sealing it therein. A technique for constructing screens, and especially security screens, which facilitated their manufacture and reliable installation would reduce the cost of initially constructing the screen and facilitate repairs thereto.